7. Of the Arithmetical Art

Seeing, however, that nearly all heresy has discovered by the art of arithmetic measures of hebdomads and certain projections of Æons, each tearing the art to pieces in different ways and only changing the names,—but of these (men) Pythagoras came to be teacher who first transmitted to the Greeks such numbers from Egypt—it seems good not to pass over this, but after briefly pointing it out to proceed to the demonstration of the objects of our enquiries. These men were arithmeticians and geometricians to whom especially it seems Pythagoras first supplied the principles (of their arts). And they took the first beginnings (of things), discovered apparently by reason alone, from the numbers which can always proceed to infinity by multiplication and the figures (produced by it). For the beginning of geometry, as may be seen, is an indivisible point; but from that point the generation of the infinite figures from the point is discovered by the art. For the point when extended in length becomes after extension a line having a point as its limit: and a line when extended in breadth produces a superficies and the limits of the superficies are lines: and a superficies extended in depth becomes a (solid) body: and when this solid is in existence, the nature of the great body is thus wholly founded from the smallest point. And this is what Simon says thus: “The little will be great, being as it were a point; but the great will be boundless,” in imitation of that geometrical point. But the beginning of arithmetic, which includes by combination philosophy, is a number which is boundless and incomprehensible, containing within itself all the numbers capable of coming to infinity by multitude. But the beginning of the numbers becomes by hypostasis the first monad, which is a male unit begetting as does a father all the other numbers. Second comes the dyad, a female number, and the same is called even by the arithmeticians. Third comes the triad, a male number; this also has been ordained to be called odd by the arithmeticians. After all these comes the tetrad, a female number, and this same is also called even, because it is female. Therefore all the numbers taken from the genus are four—but the boundless genus is number—wherefrom is constructed their perfect number, the decad. For 1, 2, 3, 4 become 10, as has before been shown, if the name which is proper to each of the numbers be substantially kept. This is the sacred Tetractys according to Pythagoras which contains within itself the roots of eternal nature, that is, all the other numbers. For the 11, 12 and the rest take the principle of birth from the 10. Of this decad, the perfect number, the four parts are called: number, monad, square and cube. The conjunctions and minglings of which are for the birth of increase, they completing naturally the fruitful number. For when this square is multiplied into itself, it becomes a square squared; but when a square into a cube, it becomes a square cubed; but when a cube into a cube, it becomes a cube cubed. So that all the numbers are seven, in order that the birth of the existing numbers may come from a hebdomad, which is number, monad, square, cube, square of a square, cube of a square, cube of a cube.

Of this hebdomad Simon and Valentinus, having altered the names, recount prodigies, hastening to base upon it their own systems. For Simon calls (it) thus: Mind, Thought, Name, Voice, Reasoning, Desire and He who has Stood, Stands and will Stand: and Valentinus: Mind, Truth, Word, Life, Man, Church and the Father who is counted with them. According to these (ideas) of those trained in the arithmetic philosophy, which they admired as something unknowable by the crowd, and in pursuance of them, they constructed the heresies excogitated by them.

Now there are some also who try to construct hebdomads from the healing art, being struck by the dissection of the brain, saying that the substance, power of paternity, and divinity of the universe can be learned from its constitution. For the brain, being the ruling part of the whole body rests calm and unmoved, containing within itself the breath. Now such a story is not incredible, but a long way from their attempted theory. For the brain when dissected has within it what is called the chamber, on each side of which are the membranes which they call wings, gently moved by the breath, and again driving the breath into the cerebellum. And the breath, passing through a certain reed-like vein, travels to the pineal gland. Near this lies the mouth of the cerebellum which receives the breath passing through and gives it up to the so-called spinal marrow. From this the whole body gets a share of pneumatic (force), all the arteries being dependent like branches on this vein, the extremity of which finishes in the genital veins. Whence also the seeds proceeding from the brain through the loins are secreted. But the shape of the cerebellum is like the head of a dragon; concerning which there is much talk among those of the Gnosis falsely so called, as we have shown. But there are other six pairs (of vessels) growing from the brain, which making their way round the head and finishing within it, connect the bodies together. But the seventh (goes) from the cerebellum to the lower parts of the rest of the body, as we have said.

And about this there is much talk since Simon and Valentinus have found in it hints which they have taken, although they do not admit it, being first cheats and then heretics. Since then it seems that we have sufficiently set out these things, and that all the apparent dogmas of earthly philosophy have been included in (these) four books, it seems fitting to proceed to their disciples or rather to their plagiarists.

The Fourth Book of Philosophumena